Reid is allowing votes on two GOP amendments, both from Republicans who voted with Democrats on Monday to end debate on the motion to proceed. Those amendment votes could happen as early as Wednesday afternoon.

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Sens. Rob Portman (R-Ohio), Kelly Ayotte (R-N.H.) and Pat Toomey (R-Pa.) were last-minute supporters of advancing the bill, which would ban workplace discrimination based on sexual orientation and gender identity. They joined four other Republicans who had announced their support ahead of the 61-30 vote.

Reid set up a vote on an amendment from Portman and Ayotte that would prevent retaliation against religious organizations that don't hire someone because of sexual orientation or identity.

“The bill's religious exemption ensures that churches and other religious employers may continue to operate according to their deeply held beliefs," Portman said. "I had concerns, however, that ENDA could leave the door open for the government to discriminate against these very groups on the basis of those beliefs. I am pleased that the bill's authors have decided to allow a vote on my amendment to prevent retaliation against religious organizations."

Toomey’s amendment would expand the religious exemption within the bill. Currently, the bill language exempts churches, but Toomey’s amendment would extend that exemption to any employer that is partially owned by a religion or has religious affiliations, including religious universities.

Democrats will also likely vote to table a motion to send the bill back to the Senate Health, Education, Labor and Pensions Committee.

Reid has said he wants to complete work on ENDA by the end of the week.

If the Republican amendments aren’t agreed to, it’s unclear if they’ll still support cloture on the bill. Democrats will need five Republicans to vote with them on ending debate on the legislation to reach the 60-vote threshold.

Sen. Jeff Merkley (D-Ore.) introduced S. 815 earlier this year. He said the legislation is necessary because more than half of states still allow discrimination based on sexual orientation or identity.

“In 29 states you can still be fired from a job and told not to apply in the beginning because of your sexual identity or orientation,” Merkley said Tuesday. “It’s time to end that discrimination and enhance the vision of equality and fairness.”

Even if his bill passes in the Senate, it’s unlikely that the House will take up the measure. Earlier this week, an official for Speaker John Boehner (R-Ohio) said the House GOP leader opposes the bill because it would increase “frivolous” lawsuits. But Merkley pointed out that his home state and several others have already had this law on the books for years and haven’t seen a large increase in unwarranted lawsuits.